You've seen contemporary dance, even if you don't think you have: it's actually been infiltrating the pop world for years. Some recent examples: Beyoncé filched great chunks of Belgian choreographer Anne Teresa De Keersmaeker's classic Rosas Danst Rosas for her Countdown video; Kylie regularly hires "serious" contemporary choreographers such as Akram Khan and Rafael Bonachela for her tours; if you go to Latitude this summer you'll see dance companies sharing the bill with Kraftwerk and Bloc Party; and the Knife had a troupe of experimental dancers on stage for this year's Shaking The Habitual tour.

A bit further off the radar, when Swedish band Lune played in London recently, choreographer Mårten Spångberg could be seen looming over singer Linnea Martinsson in flowing robes and headdress, like an escapee from a particularly unscary Halloween party. A wild-haired, large-spectacled Swede, Spångberg has been creating enthusiastically academic and absurdly cool choreography for 20 years (he's 45 now). He's noticed the pop world's interest in dance, and he's got issues.

"Why is dance so fucking conservative as a response?" he wonders. "Dance should use pop to change what dance can be, not try to make something accessible. The problem is that dance tends to hook on to the wrong part of pop. Let's climb to the top, go penthouse level and see what pop can make possible. Pop should not be about reaching the masses, it's a matter of making the masses reach for you."

Rest assured that contemporary dance, Spångberg-style, doesn't look anything like Kylie. His current piece Epic, to be performed at this year's Manchester international festival, is like being at an intimidatingly hip squat party, with guests in neon sportswear and facepaint who never go home. Across its four hours, you rarely see anything you would recognise as a conventional dance step. At one point, the troupe pick up instruments and play charmingly unaccomplished versions of songs by Bow Wow Wow and Siouxsie And The Banshees.

Epic is totally unspectacular, and quietly revolutionary. No one will tell you to turn your phone off, for a start. "Of course not!" says Spångberg. "We also have phones onstage; we have notes on our smartphones. If you take a nap or go for a smoke or want to update your Facebook, that's also totally d'accord. I'm not interested in keeping the audience busy. I'm interested in how differently we can think about audiences today, compared with, say, 20 years ago."

'The dance to come is an altogether different one, that not even I can predict'

The thinking goes that if the modern audience watches TV on laptops, while Instagramming and checking emails at the same time, why would contemporary artists ignore that and insist on trapping them in a silent black box for an hour? Rather than rail against our diminishing attention spans, Spångberg looks at this as an opportunity to explore "other kinds of attention". He's more interested in philosophy and economics and commercial culture than what's happening in other art forms. "I would say that eBay is much more of an influence to me than visual art," he declares.

In fact, Spångberg is so committed to being genuinely contemporary that he's thrown away his records and CDs and only listens to new music. The same goes for books. "For me, it's all a matter of the practising of contemporary life," he says. And that means throwing out some other old stuff too: systems, structures, the roles of artist and audience. Spångberg's shows are the dance equivalent of the Occupy movement, and not just because there are some long-haired youths sitting around on rugs with guitars. "We have to produce something that neo-liberalism doesn't know how to cope with, at all," he says. Spångberg refers to his work as choreography, not performance; there's a difference. "It's a tool for organising time and space," he explains, whereas performance is about being an entertainer. "And you are not here to be entertained."

All this means Spångberg is unlikely to have his dance moves appropriated by a leading R&B star any time soon, although after his experiences with Lune, he quite likes the idea of being a rock star. "I'm quite excited about exploring the possibilities that a rock stage can offer. It is also quite fucking fab to play in front of 12,000 people."

There is actually already a choreographer who embraces the intoxicating energy of the rock gig and gets his audience moshing in the stalls: Hofesh Shechter's full-throttle Political Mother show has a stage of drummers and electric guitars kerranging at seat-shaking volume. But this is not Spångberg's thing. He puts it less tactfully: "Absolutely totally worthless choreography." For him it's old-world stuff, about representation and not form. Spångberg wants us to question what choreography can be, not give us what we already know. "The dance to come is an altogether different one, not even I can predict," he says. Beyoncé, can you handle this?